I love the enthusiasm you showed. I have not traveled the ocean of mathematics as far as you have. I also don't intend on doing it. But I respect everybody who does so because it is the fundament of many of the natural sciences and technological disciplines.
Wow great video!!! I've been looking for textbooks to learn DG on my own and after comparing several PDF and reading some suggestions over the internet, i came up with the same two books by Lee and Tu!! Actually the one by Lee is suggested by many people, but rhe one by Tu is rather obscure, few people know about it! I'll also check out the notes by Wang 👍🏼👍🏼👍🏼
Hello! My grandfather is actually from Egypt! What type of topology are you trying to learn, point-set topology? Algebraic Topology? Or differential topology? Or a different area?
@@oceansofmath I'm really sorry that I didn't see your video that you've already made, namely "Textbook Recommendations: Response to Viewer Request". Thank you for your content!
Introduction to Smooth Manifolds has a prequel Introduction to Topological Manifolds, and also sequels on Riemannian and complex manifolds have you checked them out?
@@dureduck A couple comments. Note that this is not exactly my field of study so you should probably consult google / reddit. For an undergrad level I like Introduction to Probability by Benedek Valkó, David F. Anderson, and Timo O. Seppäläinen. This is probably similar to what you saw in your course, I took an undergrad course which followed this textbook and its pretty good. Then there are a few directions you can take; first, you can go the statistics route for which I really like Introduction to Probability and Mathematical Statistics by Bain / Engelhardt. This is a great intermediate level textbook with a ton of exercises. If you want to go more of the pure math (advanced) route, then you will need to learn measure theory as a prerequisite. I recommend Measure Theory by Halmos, and you will need some knowledge of real analysis (see my video, I recommend Taylor or Folland). Once you have a little background in measure theory, and the key integration theorems from real analysis (Monotone Convergence Theorem, Lebesgue Dominated Convergence Theorem, Modes of Convergence, etc) (note also Terrence Tao has some good comments on his website about modes of convergence), THEN you are more prepared to tackle a graduate probability textbook. I have not read such a textbook, consulting reddit one such textbook is Probability: Theory and Examples by Rick Durrett. Again, I have not actually taken a grad course in probability nor have I studied the book by Durrett, but I do know for an absolute fact that you will need the prerequisites of measure theory and real analysis.
Funny I recently found the book by Anderson on sale at half price and bought it! I checked the pdf and it looked like a great introduction, it's great to see it's recommended by you!
funny that this appears in my recommended... I read Lee's Intro to Smooth manifolds for my undergraduate dissertation! Great book, the bible of manifold theory
Manifolds always remind me of my Dad and the Hot Rods he & his Buddies worked on.
I love the enthusiasm you showed. I have not traveled the ocean of mathematics as far as you have. I also don't intend on doing it. But I respect everybody who does so because it is the fundament of many of the natural sciences and technological disciplines.
Impressive one hand filming + one hand turning pages at the beginning lol thanks for the tip on the lecture notes!
Wow great video!!! I've been looking for textbooks to learn DG on my own and after comparing several PDF and reading some suggestions over the internet, i came up with the same two books by Lee and Tu!! Actually the one by Lee is suggested by many people, but rhe one by Tu is rather obscure, few people know about it! I'll also check out the notes by Wang 👍🏼👍🏼👍🏼
I'm really waiting your topology textbook recommendation video. Your follower from Egypt!
Hello! My grandfather is actually from Egypt! What type of topology are you trying to learn, point-set topology? Algebraic Topology? Or differential topology? Or a different area?
@@oceansofmath
Wow :)
I'm currently learning point set topology aka general topology then I may go for differential topology as the next step.
@@oceansofmath I'm really sorry that I didn't see your video that you've already made, namely "Textbook Recommendations: Response to Viewer Request". Thank you for your content!
Introduction to Smooth Manifolds has a prequel Introduction to Topological Manifolds, and also sequels on Riemannian and complex manifolds have you checked them out?
You are referencing the book by Lee? If so, I will definitely have to check them out, thanks!
Also the books by Loring Tu are part of a quadrilogy! @oceansofmath
@@oceansofmath the book by Losing Tu is part of a quadrilogy!
thanks for the video! any recs for probability textbooks or resources?
Hello! What level of probability? I have several possible recommendations depending on the prerequisite mathematical background.
Took one undergrad intro to probs and stats and would like to learn more. Would greatly appreciate beginner to intermediate level book. Thank you!
@@dureduck A couple comments. Note that this is not exactly my field of study so you should probably consult google / reddit. For an undergrad level I like
Introduction to Probability by Benedek Valkó, David F. Anderson, and Timo O. Seppäläinen. This is probably similar to what you saw in your course, I took an undergrad course which followed this textbook and its pretty good. Then there are a few directions you can take; first, you can go the statistics route for which I really like Introduction to Probability and Mathematical Statistics by Bain / Engelhardt. This is a great intermediate level textbook with a ton of exercises. If you want to go more of the pure math (advanced) route, then you will need to learn measure theory as a prerequisite. I recommend Measure Theory by Halmos, and you will need some knowledge of real analysis (see my video, I recommend Taylor or Folland). Once you have a little background in measure theory, and the key integration theorems from real analysis (Monotone Convergence Theorem, Lebesgue Dominated Convergence Theorem, Modes of Convergence, etc) (note also Terrence Tao has some good comments on his website about modes of convergence), THEN you are more prepared to tackle a graduate probability textbook. I have not read such a textbook, consulting reddit one such textbook is Probability: Theory and Examples by Rick Durrett. Again, I have not actually taken a grad course in probability nor have I studied the book by Durrett, but I do know for an absolute fact that you will need the prerequisites of measure theory and real analysis.
Funny I recently found the book by Anderson on sale at half price and bought it! I checked the pdf and it looked like a great introduction, it's great to see it's recommended by you!
"Springer Verlag" is German for "This is gonna hurt *and* you're gonna pay for it!"
But Springer will take your flakey LaTex and fix it right up. Penguin won't do that.
@@davidjohnston4240 Springer books are well-made, that's for sure.
funny that this appears in my recommended... I read Lee's Intro to Smooth manifolds for my undergraduate dissertation! Great book, the bible of manifold theory
I don’t know what a manifold is, but I like them smooth
thanks dude
Kudos
Good
The topological adventures of the mind...